A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 46 semigroups of order six, all of which generate the variety V[7382]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-d64e044a11f9dae6 in the data of the bases-min seal.
Certified for
[6, 7382] [6, 7440] [6, 7441] [6, 7477] [6, 7503] [6, 7706] [6, 7730] [6, 7789] [6, 7827] [6, 7828] [6, 7854] [6, 7986] [6, 7988] [6, 8032] [6, 8059] [6, 8273] [6, 8524] [6, 8533] [6, 8546] [6, 8770] [6, 8775] [6, 10154] [6, 10326] [6, 10926] [6, 10927] [6, 10937] [6, 11355] [6, 12582] [6, 12645] [6, 12767] [6, 12837] [6, 12854] [6, 12855] [6, 13002] [6, 13018] [6, 13019] [6, 13022] [6, 13023] [6, 13055] [6, 13057] [6, 13427] [6, 13428] [6, 13430] [6, 13621] [6, 13942] [6, 14243]
The identities
- x² ≈ x³
- xyx ≈ yx²